Problem 4
Question
Approximate each number using a calculator. Round your answer to three decimal places. $$5^{\sqrt{3}}$$
Step-by-Step Solution
Verified Answer
The answer will depend on the calculator used, but it should be a number rounded to the nearest three decimal places.
1Step 1: Input the Main Expression into the Calculator
First, the expression \(5^{\sqrt{3}}\) should be entered into the calculator.
2Step 2: Perform the Calculation
After entering the expression into the calculator, the Calculate or Equals button is pressed which will give a number, this number is the unrounded result.
3Step 3: Rounding the Result
Finally, the obtained result should be rounded to three decimal places according to standard rounding rules. If the fourth digit after the decimal point is 5 or more, the third digit is increased by one. If it's less than 5, the third digit remains the same.
Key Concepts
Calculator Usage
Calculator Usage
Calculators are essential tools for students working with complex numbers and expressions, particularly when dealing with exponents and roots. They help simplify and speed up calculations that would otherwise be cumbersome by hand.
To use a calculator effectively, one needs to be familiar with the specific input methods for different mathematical operations. For instance, when inputting the expression like in our example exercise, namely \(5^{\sqrt{3}}\), you need to know how to enter the square root and exponentiation functions. Most scientific calculators have dedicated buttons for these functions—often labeled as \
To use a calculator effectively, one needs to be familiar with the specific input methods for different mathematical operations. For instance, when inputting the expression like in our example exercise, namely \(5^{\sqrt{3}}\), you need to know how to enter the square root and exponentiation functions. Most scientific calculators have dedicated buttons for these functions—often labeled as \
Other exercises in this chapter
Problem 4
Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
View solution Problem 4
Write each equation in its equivalent exponential form. $$2=\log _{9} x$$
View solution Problem 5
Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$2^{2 x-1}=32$$
View solution Problem 5
Use properties of logarithms to expand logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
View solution